SOLUTION: Given a normal distribution with u=100 and q=10, if you select a sample of n=25, what is the probability that x bar is: a. less than 95 b. between 95 and 97.5 c. above 102.2 d.

Algebra ->  Probability-and-statistics -> SOLUTION: Given a normal distribution with u=100 and q=10, if you select a sample of n=25, what is the probability that x bar is: a. less than 95 b. between 95 and 97.5 c. above 102.2 d.      Log On


   

Question 905056: Given a normal distribution with u=100 and q=10, if you select a sample of n=25, what is the probability that x bar is:
a. less than 95
b. between 95 and 97.5
c. above 102.2
d. there is a 65% chance that Xbar is above what value?
I am trying to use the excel functions and it's not working. Thank you so much
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

really recommend us TI Calculator. 

However, z values are easy enough manually, and then going to Excel NORMSDIST(z)  

a. less than 95: P(z < (95-100)/10/sqrt(25) = P(z < -5/2) =NORMSDIST(-2.5)= .0062 

b. between 95 and 97.5: P(z< -1.25 - P(z< -2.5)= .1057 -.0062

TI ,makes this so easy) normalcdf(-2.5, -1.25)

c. above 102.2 = 1 -P(z < 1.1)= 1- .8643



d. there is a 65% chance that Xbar is above what value X? 

invNorm(.45) Or Excel NORMSINV(.45)= -.1257 = z

-.1257 = (X-100)/10/sqrt(25)

2(-.1257) + 100 = X